Bulletin des Sciences Mathematiques最新文献

{"title":"An Ext-Tor duality theorem, cohomological dimension, and applications","authors":"Rafael Holanda ,&nbsp;Cleto B. Miranda-Neto","doi":"10.1016/j.bulsci.2025.103696","DOIUrl":"10.1016/j.bulsci.2025.103696","url":null,"abstract":"<div><div>We provide a duality theorem between Ext and Tor modules over a Cohen-Macaulay local ring possessing a canonical module, and use it to prove some freeness criteria for finite modules. The applications include a characterization of codimension three complete intersection ideals and progress on a long-held multi-conjecture of Vasconcelos. By a similar technique, we furnish another theorem which in addition makes use of the notion of cohomological dimension and is mainly of interest in dimension one; as an application, we show that the (still open) complete intersection case of the celebrated Huneke-Wiegand conjecture holds true provided that a single finiteness condition is satisfied.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103696"},"PeriodicalIF":1.3,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rational solutions of parametric first-order algebraic differential equations","authors":"Sebastian Falkensteiner ,&nbsp;J. Rafael Sendra","doi":"10.1016/j.bulsci.2025.103694","DOIUrl":"10.1016/j.bulsci.2025.103694","url":null,"abstract":"<div><div>In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the existence of rational solutions of the differential equation, with parametric coefficients, when the parameters are specialized.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103694"},"PeriodicalIF":1.3,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144535616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The topology and isochronicity on complex Hamiltonian systems with homogeneous nonlinearities","authors":"Guangfeng Dong ,&nbsp;Jiazhong Yang","doi":"10.1016/j.bulsci.2025.103695","DOIUrl":"10.1016/j.bulsci.2025.103695","url":null,"abstract":"<div><div>In this paper, we study the Hamiltonian vector fields with homogeneous nonlinear parts on <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Firstly, we present a series of topological properties of the polynomial Hamiltonian function, with a particular focus on the characteristics of critical points and non-trivial cycles that vanish at infinity. Secondly, we use these topological properties to derive a complete set of necessary and sufficient conditions of isochronous centers for this class of systems of any degree. These conditions indicate that the isochronous center variety has two different components in the coefficient space of the nonlinear parts and each component is the intersection of several hyperplanes.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103695"},"PeriodicalIF":1.3,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Perturbative global solutions of a large class of cross diffusion systems in any dimension","authors":"L. Desvillettes ,&nbsp;A. Moussa","doi":"10.1016/j.bulsci.2025.103686","DOIUrl":"10.1016/j.bulsci.2025.103686","url":null,"abstract":"<div><div>This article focuses on a large family of cross-diffusion systems of the form <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>U</mi><mo>−</mo><mi>Δ</mi><mi>A</mi><mo>(</mo><mi>U</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, in dimension <span><math><mi>d</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, and where <span><math><mi>U</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We show that under natural conditions on the nonlinearity <em>A</em>, those systems have a unique smooth (nonnegative for all components) solution when the initial data are small enough in a suitable norm.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103686"},"PeriodicalIF":1.3,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Real interpolation for martingale Orlicz-Lorentz-Karamata Hardy spaces","authors":"Zhiwei Hao ,&nbsp;Libo Li ,&nbsp;Ferenc Weisz","doi":"10.1016/j.bulsci.2025.103690","DOIUrl":"10.1016/j.bulsci.2025.103690","url":null,"abstract":"<div><div>We introduce a new class of Orlicz-Lorentz-Karamata spaces and develop the martingale theory in this framework. More precisely, we study the real interpolation theory for Orlicz-Lorentz-Karamata spaces as well as for the corresponding martingale Hardy spaces. As a consequence, the generalization of Doob's maximal inequality will be proved. Moreover, the atomic decompositions of the martingale Hardy Orlicz-Lorentz-Karamata spaces are also established. With the help of atomic decompositions, the duality and generalized John-Nirenberg theorem for martingale Hardy Orlicz-Lorentz-Karamata spaces are presented.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103690"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak differentiability for commutators of multilinear maximal functions of Sobolev functions on domains","authors":"Feng Liu ,&nbsp;Xiao Zhang","doi":"10.1016/j.bulsci.2025.103691","DOIUrl":"10.1016/j.bulsci.2025.103691","url":null,"abstract":"<div><div>A systematic study is given for weak differentiability for the commutators of multilinear maximal operators and multilinear maximal commutators associated with a vector-valued function <span><math><mover><mrow><mi>b</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></math></span> as well as their fractional variants on domains, where each <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> belongs to Lipschitz space. The bounds and continuity for the above commutators are established on the first order Sobolev spaces. The bounds for the above commutators are also proved on the Sobolev spaces with zero boundary values.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103691"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On compactness of commutators of the Christ-Journé type operators","authors":"Qianqian Zhang ,&nbsp;Moyan Qin ,&nbsp;Shifen Wang ,&nbsp;Qingying Xue","doi":"10.1016/j.bulsci.2025.103692","DOIUrl":"10.1016/j.bulsci.2025.103692","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper investigates the commutators &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; associated with Christ-Journé type operator&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;p.v.&lt;/mtext&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We show that &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is bounded on &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; whenever &lt;span&gt;&lt;math&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;BMO&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and compact on &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; whenever &lt;span&gt;&lt;math&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;CMO&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;CMO&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the closure of &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; in the &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;BMO&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; topology. Furthermore, we also study Christ-Journé type commutators with rough kernels &lt;span&gt;&lt;math&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, denoted by &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103692"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-dimensional Bohr radii of Banach space valued holomorphic functions","authors":"Shankey Kumar ,&nbsp;Ramesh Manna","doi":"10.1016/j.bulsci.2025.103688","DOIUrl":"10.1016/j.bulsci.2025.103688","url":null,"abstract":"<div><div>In this article, we study the multi-dimensional Bohr radii of holomorphic functions defined on the Banach sequence spaces with values in the Banach spaces. For the case of finite dimensional Banach spaces, we exhibit the exact asymptotic growth of the Bohr radius. To achieve our goal in the finite case, we use <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math></span>-summability of certain coefficients of a given polynomial in terms of its uniform norm on <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>. The infinite case is handled using the techniques developed in recent years from the work of Defant, Maestre and Schwarting. We crucially use several properties of the symmetric <em>M</em>-linear mapping associated with a homogeneous polynomial of degree <em>M</em> in our analysis. Furthermore, we study the bounds of the arithmetic Bohr radius of Banach space-valued holomorphic functions defined on the Banach sequence spaces, which generalizes the work of Defant, Maestre, and Prengel in this direction.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103688"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kernel projection operator's approximation error estimation in weighted mixed-norm shift-invariant subspaces","authors":"Junjian Zhao","doi":"10.1016/j.bulsci.2025.103689","DOIUrl":"10.1016/j.bulsci.2025.103689","url":null,"abstract":"<div><div>By utilizing the Strang-Fix theory, approximation of non-decaying signals from shift-invariant subspaces (<span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-norm) is studied by Nguyen and Unser (2019) <span><span>[42]</span></span>. The non-decaying function can be seemed as a kind of weighted function. In this paper, using the weighted mixed-norm Wiener amalgam space and hybrid space, we will study the approximation error bounds of the kernel projection operator in the weighted mixed-norm sense without Strang-Fix theory. Note that the condition under weighted mixed-norm hybrid space is weaker than that of Wiener amalgam space. So, in this paper, not only based on the Wiener amalgam space, we will also demonstrate that, as a comparison, the approximation results of the projection operator are also valid under the relevant hybrid space.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103689"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Invariant vector bundles and Hitchin systems","authors":"Zakaria Ouaras ,&nbsp;Hacen Zelaci","doi":"10.1016/j.bulsci.2025.103687","DOIUrl":"10.1016/j.bulsci.2025.103687","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi><mo>→</mo><mi>Y</mi></math></span> be a Galois cover with Galois group Γ, where <em>X</em> and <em>Y</em> are smooth complex projective curve of genus ⩾2. In this paper, we study the moduli spaces of semistable Γ-invariant vector bundles on <em>X</em> and classify their connected components. We also study the Hitchin systems on these moduli spaces and determine their fibers in the smooth case.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103687"},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}